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% like mgram2, except we unroll the DBN so we can use smaller
% state spaces for the early duration nodes:
% the state spaces are D1 in {1}, D2 in {1,2}
past = 1;
words = {'the', 't', 'h', 'e'};
data = 'the';
nwords = length(words);
word_len = zeros(1, nwords);
word_prob = normalise(ones(1,nwords));
word_logprob = log(word_prob);
for wi=1:nwords
word_len(wi)=length(words{wi});
end
D = max(word_len);
alphasize = 26*2;
data = letter2num(data);
T = length(data);
% node numbers
W = 1; % top level state = word id
L = 2; % bottom level state = letter position within word
F = 3;
O = 4;
ss = 4;
intra = zeros(ss,ss);
intra(W,[F L O])=1;
intra(L,[O F])=1;
inter = zeros(ss,ss);
inter(W,W)=1;
inter(L,L)=1;
inter(F,[W L O])=1;
T = 3;
dag = unroll_dbn_topology(intra, inter, T);
% node sizes
ns = zeros(1,ss);
ns(W) = nwords;
ns(L) = D;
ns(F) = 2;
ns(O) = alphasize;
ns = repmat(ns(:), [1 T]);
for d=1:D
ns(d,L)=d; % max duration
end
ns = ns(:);
% Equiv class in brackets for D=3
% The Lt's are not tied until t>=D, since they have different sizes.
% W1 and W2 are not tied since they have different parent sets.
% W1 (1) W2 (5) W3 (5) W4 (5)
% L1 (2) L2 (6) L3 (7) L4 (7)
% F1 (3) F2 (3) F3 (4) F3 (4)
% O1 (4) O2 (4) O2 (4) O4 (4)
% Since we are not learning, we can dispense with tying
% Make the bnet
Wnodes = unroll_set(W, ss, T);
Lnodes = unroll_set(L, ss, T);
Fnodes = unroll_set(F, ss, T);
Onodes = unroll_set(O, ss, T);
bnet = mk_bnet(dag, ns);
eclass = bnet.equiv_class;
% uniform start distrib over words, uniform trans mat
Wstart = normalise(ones(1,nwords));
Wtrans = mk_stochastic(ones(nwords,nwords));
bnet.CPD{eclass(Wnodes(1))} = tabular_CPD(bnet, Wnodes(1), 'CPT', Wstart);
for t=2:T
bnet.CPD{eclass(Wnodes(t))} = hhmmQ_CPD(bnet, Wnodes(t), 'Fbelow', Fnodes(t-1), ...
'startprob', Wstart, 'transprob', Wtrans);
end
% always start in state d = length(word) for each bottom level HMM
% and then count down
% make downcounters
RLtrans = mk_rightleft_transmat(D, 0); % 0 self loop prob
Ltrans = repmat(RLtrans, [1 1 nwords]);
for t=1:T
Lstart = zeros(nwords, min(t,D));
for i=1:nwords
l = length(words{i});
Lstart(i,l)=1;
if d==1
bnet.CPD{eclass(Lnodes(1))} = tabular_CPD(bnet, Lnodes(1), 'CPT', Lstart);
else
bnet.CPD{eclass(Lnodes(t))} = hhmmQ_CPD(bnet, Lnodes(t), 'Fself', Fnodes(t-1), 'Qps', Wnodes(t), ...
'startprob', Lstart, 'transprob', Ltrans);
end
end
end
% Finish when downcoutner = 1
Fprob = zeros(nwords, D, 2);
Fprob(:,1,2)=1;
Fprob(:,2:end,1)=1;
% Define CPDs for slice
bnet.CPD{eclass(W,1)} = tabular_CPD(bnet, W, 'CPT', Wstart);
bnet.CPD{eclass(L,1)} = tabular_CPD(bnet, L, 'CPT', Lstart);
bnet.CPD{eclass(F,1)} = tabular_CPD(bnet, F, 'CPT', Fprob);
% Define CPDs for slice 2
bnet.CPD{eclass(W,2)} = hhmmQ_CPD(bnet, W+ss, 'Fbelow', F, 'startprob', Wstart, 'transprob', Wtrans);
bnet.CPD{eclass(L,2)} = hhmmQ_CPD(bnet, L+ss, 'Fself', F, 'Qps', W+ss, 'startprob', Lstart, 'transprob', Ltrans);
if 0
% To test it is generating correctly, we create an artificial
% observation process that capitalizes at the start of a new segment
% Oprob(Ft-1,Qt,Dt,Yt)
Oprob = zeros(2,nwords,D,alphasize);
Oprob(1,1,3,letter2num('t'),1)=1;
Oprob(1,1,2,letter2num('h'),1)=1;
Oprob(1,1,1,letter2num('e'),1)=1;
Oprob(2,1,3,letter2num('T'),1)=1;
Oprob(2,1,2,letter2num('H'),1)=1;
Oprob(2,1,1,letter2num('E'),1)=1;
Oprob(1,2,1,letter2num('a'),1)=1;
Oprob(2,2,1,letter2num('A'),1)=1;
Oprob(1,3,1,letter2num('b'),1)=1;
Oprob(2,3,1,letter2num('B'),1)=1;
Oprob(1,4,1,letter2num('c'),1)=1;
Oprob(2,4,1,letter2num('C'),1)=1;
% Oprob1(Qt,Dt,Yt)
Oprob1 = zeros(nwords,D,alphasize);
Oprob1(1,3,letter2num('t'),1)=1;
Oprob1(1,2,letter2num('h'),1)=1;
Oprob1(1,1,letter2num('e'),1)=1;
Oprob1(2,1,letter2num('a'),1)=1;
Oprob1(3,1,letter2num('b'),1)=1;
Oprob1(4,1,letter2num('c'),1)=1;
bnet.CPD{eclass(O,2)} = tabular_CPD(bnet, O+ss, 'CPT', Oprob);
bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', Oprob1);
evidence = cell(ss,T);
%evidence{W,1}=1;
sample = cell2num(sample_dbn(bnet, 'length', T, 'evidence', evidence));
str = num2letter(sample(4,:))
end
[log_obslik, obslik, match] = mk_mgram_obslik(lower(data), words, word_len, word_prob);
% obslik(j,t,d)
softCPDpot = cell(ss,T);
ens = ns;
ens(O)=1;
ens2 = [ens ens];
for t=2:T
dom = [F W+ss L+ss O+ss];
% tab(Ft-1, Q2, Dt)
tab = ones(2, nwords, D);
if past
tab(1,:,:)=1; % if haven't finished previous word, likelihood is 1
%tab(2,:,:) = squeeze(obslik(:,t,:)); % otherwise likelihood of this segment
for d=1:min(t,D)
tab(2,:,d) = squeeze(obslik(:,t,d));
end
else
for d=1:max(1,min(D,T+1-t))
tab(2,:,d) = squeeze(obslik(:,t+d-1,d));
end
end
softCPDpot{O,t} = dpot(dom, ens2(dom), tab);
end
t = 1;
dom = [W L O];
% tab(Q2, Dt)
tab = ones(nwords, D);
if past
%tab = squeeze(obslik(:,t,:));
tab(:,1) = squeeze(obslik(:,t,1));
else
for d=1:min(D,T-t)
tab(:,d) = squeeze(obslik(:,t+d-1,d));
end
end
softCPDpot{O,t} = dpot(dom, ens(dom), tab);
%bnet.observed = [];
% uniformative observations
%bnet.CPD{eclass(O,2)} = tabular_CPD(bnet, O+ss, 'CPT', mk_stochastic(ones(2,nwords,D,alphasize)));
%bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', mk_stochastic(ones(nwords,D,alphasize)));
engine = jtree_dbn_inf_engine(bnet);
evidence = cell(ss,T);
% we add dummy data to O to force its effective size to be 1.
% The actual values have already been incorporated into softCPDpot
evidence(O,:) = num2cell(ones(1,T));
[engine, ll_dbn] = enter_evidence(engine, evidence, 'softCPDpot', softCPDpot);
%evidence(F,:) = num2cell(2*ones(1,T));
%[engine, ll_dbn] = enter_evidence(engine, evidence);
gamma = zeros(nwords, T);
for t=1:T
m = marginal_nodes(engine, [W F], t);
gamma(:,t) = m.T(:,2);
end
gamma
xidbn = zeros(nwords, nwords);
for t=1:T-1
m = marginal_nodes(engine, [W F W+ss], t);
xidbn = xidbn + squeeze(m.T(:,2,:));
end
% thee
% xidbn(1,4) = 0.9412 the->e
% (2,3)=0.0588 t->h
% (3,4)=0.0588 h-e
% (4,4)=0.0588 e-e
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